Obscured by the swirl of rhetoric over huge budget deficits is a major accomplishment already being achieved by President Reagan's embattled economic program.

The growth rate of federal government spending, notes Sen. Pete V. Domenici (R) of New Mexico, has been markedly slowed by Mr. Reagan's 1982 budget - from 14.5 percent in recent years to 9 percent now.

The President may or may not be able to reach his goal of reducing the annual growth rate to 6.5 percent. But the trend is downward, a trend welcomed by many Democrats as well as Republicans.

''I happen to believe,'' said Rep. James R. Jones (D) of Oklahoma, chairman of the House Budget Committee, in an interview earlier this year, ''that a dramatic change in fiscal policy is long overdue and I share the (Reagan budget-cutting) goals.''

If, however, Mr. Reagan hopes to preserve and tighten his grasp on government spending, he may have to reverse himself and agree to sizable tax increases over the next few years.

Otherwise, experts agree, budget deficits will grow so rapidly that interest payments on new Treasury borrowings, coupled with outlays to combat recession, could wipe out White House gains on controlling government spending.

So far the President insists that the way to pump fresh vigor into the economy is to cut taxes, not raise them. This was the rationale behind his 25 percent across-the-board income tax cut program, spread over three years.

Since then the House has talked about several minor ''revenue enhancers,'' including higher excise taxes on cigarettes and alcohol, user fees on boat owners to offset Coast Guard costs, and more rigorous collection of taxes by the Internal Revenue Service.

Republican leaders now tell the President that this will not be enough, since Congress is in no mood to get additional savings by slashing the 1982 budget again.

If, in other words, the President is to keep some kind of rein on budget deficits over the next three years, some taxes will have to be raised - perhaps as much as $60 billion or $70 billion worth.

Assuming Mr. Reagan is willing to do this, Republicans in Congress think they can get - over the 1982-84 period - another $50 billion or so in additional spending cuts.

This would add up to a package of $115 billion, with the major budget trims to be postponed until 1983 and 1984.

Estimates of the 1982 budget deficit, meanwhile - which the President had hoped to hold to $43 billion - range from $80 billion, mentioned by Senate majority leader Howard H. Baker Jr. (R) of Tennessee, to as much as $100 billion cited by Mr. Jones.

David A. Stockman, director of the Office of Management and Budget (OMB), now concedes that balancing the budget by 1984 - Mr. Reagan's original goal - will be very hard to achieve.

Mr. Stockman and other White House officials increasingly emphasize the need to cut the growth rate of government spending, rather than to balance the budget per se.

This represents a first step toward revising the economic strategy with which Mr. Reagan swept into office and which he translated into massive tax and budget cuts approved by Congress last summer.

Because the economy has so far failed to respond as the Reagan advisers hoped , and because Congress is reluctant to cut more deeply into social programs, an increase in taxes may be required.

Ways in which this might be done include postponement of the scheduled July 1983 income tax cut, a tax on imported oil, higher federal taxes on gasoline, and stepped-up decontrol of natural gas, accompanied by a windfall profits tax on decontrolled gas.